The hybrid SZ power spectrum: Combining cluster counts and SZ fluctuations to probe gas physics

Sunyaev-Zeldovich (SZ) effect from a cosmological distribution of clusters carry information on the underlying cosmology as well as the cluster gas physics. In order to study either cosmology or clusters one needs to break the degeneracies between the two. We present a toy model showing how complementary informations from SZ power spectrum and the SZ flux counts, both obtained from upcoming SZ cluster surveys, can be used to mitigate the strong cosmological influence (especially that of sigma_8) on the SZ fluctuations. Once the strong dependence of the cluster SZ power spectrum on sigma_8 is diluted, the cluster power spectrum can be used as a tool in studying cluster gas structure and evolution. The method relies on the ability to write the Poisson contribution to the SZ power spectrum in terms the observed SZ flux counts. We test the toy model by applying the idea to simulations of SZ surveys.Comment: 12 pages. 11 plots. MNRAS submitte

Extragalactic millimeter-wave point source catalog, number counts and statistics from 771 square degrees of the SPT-SZ Survey

We present a point source catalog from 771 square degrees of the South Pole Telescope Sunyaev Zel'dovich (SPT-SZ) survey at 95, 150, and 220 GHz. We detect 1545 sources above 4.5 sigma significance in at least one band. Based on their relative brightness between survey bands, we classify the sources into two populations, one dominated by synchrotron emission from active galactic nuclei, and one dominated by thermal emission from dust-enshrouded star-forming galaxies. We find 1238 synchrotron and 307 dusty sources. We cross-match all sources against external catalogs and find 189 unidentified synchrotron sources and 189 unidentified dusty sources. The dusty sources without counterparts are good candidates for high-redshift, strongly lensed submillimeter galaxies. We derive number counts for each population from 1 Jy down to roughly 9, 5, and 11 mJy at 95, 150, and 220 GHz. We compare these counts with galaxy population models and find that none of the models we consider for either population provide a good fit to the measured counts in all three bands. The disparities imply that these measurements will be an important input to the next generation of millimeter-wave extragalactic source population models.Comment: 23 pages, 8 figures, submitted to Ap

Lossy Compression with Privacy Constraints: Optimality of Polar Codes

A lossy source coding problem with privacy constraint is studied in which two correlated discrete sources $X$ and $Y$ are compressed into a reconstruction $\hat{X}$ with some prescribed distortion $D$. In addition, a privacy constraint is specified as the equivocation between the lossy reconstruction $\hat{X}$ and $Y$. This models the situation where a certain amount of source information from one user is provided as utility (given by the fidelity of its reconstruction) to another user or the public, while some other correlated part of the source information $Y$ must be kept private. In this work, we show that polar codes are able, possibly with the aid of time sharing, to achieve any point in the optimal rate-distortion-equivocation region identified by Yamamoto, thus providing a constructive scheme that obtains the optimal tradeoff between utility and privacy in this framework.Comment: Submitted for publicatio

Source Galerkin Calculations in Scalar Field Theory

In this paper, we extend previous work on scalar $\phi^4$ theory using the Source Galerkin method. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using polynomial expansions for the generating functional $Z$, we calculate propagators and mass-gaps for a number of systems. These calculations are straightforward to perform and are executed rapidly compared to Monte Carlo. The bulk of the computation involves a single matrix inversion. The use of polynomial expansions illustrates in a clear and simple way the ideas of the Source Galerkin method. But at the same time, this choice has serious limitations. Even after exploiting symmetries, the size of calculations become prohibitive except for small systems. The calculations in this paper were made on a workstation of modest power using a fourth order polynomial expansion for lattices of size $8^2$,$4^3$,$2^4$ in $2D$, $3D$, and $4D$. In addition, we present an alternative to the Galerkin procedure that results in sparse matrices to invert.Comment: 31 pages, latex, figures separat